Problem: Is ${534178}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{5341} {78} = \gray{5341} \gray{00} + {78} $ Because $534100$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${78}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $78$ , divisible by $4$ No, $78$ is not divisible by $4$, so $534178$ is also not divisible by $4$.